Unit Planning Guide: Grade ___ Unit ___ of ___
Total Page：16
File Type：pdf, Size：1020Kb
Unit Planning Guide: Grade 6 Unit 2 of 7
Unit Title: Ratios and Proportions Pacing (Duration of Unit): 7 weeks
Desired Results
Transfer Goals (Priority practice standards in bold)
Students will be able to independently use their learning to: MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning.
Established Goals (2011 MA Curriculum Frameworks Standards Incorporating the Common Core State Standards)
WIDA for English Language Learners Prerequisite Standards: Standard 1: ELLs communicate for Social and Instructional purposes within the school setting 5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions. Standard 3: ELLs communicate information, 5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. ideas and concepts necessary for academic 5.MD.1: Convert among different-sized standard measurement units within a given measurement system (e.g., success in the content area of Mathematics convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. In the lesson planning stage, teachers will need to differentiate lessons for ELLs. In order to Standards (Priority Standards in bold): accomplish this they will need: 1.) this curriculum map, 2.) a list of their ELLs and their 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two proficiency levels, and 3.) appropriate language quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings function expectations and scaffolds or there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” supports. 6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
Page 1 Unit Planning Guide: Grade 6 Unit 2 of 7 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. o 6.RP.3a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. o 6.RP.3b: Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? o 6.RP.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. o 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. o 6.RP.MA.3e: Solve problems that relate the mass of an object to its volume.
Meaning (*Mostly assessed through Performance Tasks/Assessments)
Big Ideas: (Statements and concepts written in teacher friendly language which reflect Essential Questions: (Questions which frame ongoing and important inquires about the the important [but not obvious] generalizations we want students to be able to arrive big ideas. They are written for students and used in daily instruction to help engage at. These are used by the teacher to focus daily instruction.) students in meaningful thinking.)
Proportional reasoning is used when describing the thinking that has been ap- How does proportional reasoning influence your daily life? plied to the solution of problems that involve multiplicative relationships. How do ratio and rate connect to whole number multiplication and division? A ratio is a number that relates two quantities or measures within a given sit- uation in a multiplicative relationship (in contrast to a difference or additive relationship). The relationships and rules govern whole numbers, govern all rational numbers. Making explicit the types of relationships that exist between two values will minimize confusion between multiplicative and additive situations. Ratios can express comparisons of a part to whole (a/b with b ≠ 0), for example, the ratio of the number of boys in a class to the number of students in the class.
Acquisition (*Mostly assessed through traditional summative assessments)
Page 2 Unit Planning Guide: Grade 6 Unit 2 of 7
Knowledge: Key basic concepts, facts, and key terms (written in phrases) students Skills: The discrete skills and process students should be able to use independently. should be able to recall independently. Students will be skilled at: Students will know … Identifying relationships between quantities. That a ratio describes the relationship between two quantities. Explaining that rate is a comparison of two quantities of different units, usually ex- That a ratio can be written as a unit rate. pressed as a fraction. That rate and ratio reasoning can be used to solve real world problems using tables of Giving examples of a ratio as a comparison of two quantities or measures. equivalent ratios, tape diagrams, double number line diagrams or equations. Identifying that unit rates as a comparison of a quantity to one whole (common That ratios can be used to make conversions. unit rates are cost per item or distance per time). That a percent can be described as a rate per 100. Identifying, distinguishing and explaining part-to-part and part-to-whole, and Key Academic Vocabulary: whole-to-whole relationships. bar model Representing ratios as a fraction, with a colon, or with words. constant speed Using whole-to-whole relationships to make comparisons between two different double number line diagram measures. equivalent ratios unit rate plot proportion quadrants rate ratio
Page 3 Unit Planning Guide: Grade 6 Unit 2 of 7 Knowledge Questions:
What is a ratio? What is a rate? How do you use a ratio to describe the relationship between two quantities? What are the similarities and differences between ratios, rates, and unit rates? How do you use ratio and rate reasoning to solve real-world and mathematical problems? How do you determine the percent of a quantity? How do you solve unit rate problems including those involving unit pricing and constant speed?
Resource Suggestions: CCSS Vocabulary: www.ncesd.org/page/983
Drills: www.learningfarm.com
Standard(s) Link 6.RP.1 http://learnzillion.com/lessons/580-visualize-parttopart-ratios-using-pictures
https://www.illustrativemathematics.org/6.RP.A.1
6.RP.2 http://learnzillion.com/lessons/839-understand-rates-as-a-type-of-ratio
https://www.illustrativemathematics.org/6.RP.A.2 6.RP.3a http://learnzillion.com/lessons/608-solve-missing-values-in-ratio-problems-using-a-table
https://www.illustrativemathematics.org/6.RP.A.3.a
6.RP.3b http://learnzillion.com/lessons/612-solve-for-missing-values-in-rate-problems-using-a-table
Page 4 Unit Planning Guide: Grade 6 Unit 2 of 7 https://www.illustrativemathematics.org/6.RP.A.3.b
6.RP.3c http://learnzillion.com/lessons/593-define-percents-as-ratios
https://www.illustrativemathematics.org/6.RP.A.3.c
6.RP.3d http://learnzillion.com/lessons/586-solve-ratio-problems-using-tables-and-addition
No Illustrative Math tasks for this standard yet
6.RP.3MA.e
Technology (VIDEOS)
Khan Academy http://www.khanacademy.org/math/cc-sixth-grade-math
Standard Link
6.RP.1, 6.RP.2 http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-describing-ratios
6.RP.3.a http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-ratio-word-problems
6.RP.3.b http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-rates
6.RP.3.c http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percentages http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/percent_word_problems
6.RP.3.d http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-unit-conversion
Page 5 Unit Planning Guide: Grade 6 Unit 2 of 7 GO MATH PROGRAM (STANDARDS: 6RP1; 6RP2; 6RP3a, b, c, d)
Standard(s) Lesson Lesson Title Covered Number
6RP1 4.1 Model Ratios
6RP2 4.2 Ratios & Rates
6RP3a 4.3 Equivalent Ratios & Multiplication Tables
6RP3a 4.4 Use Tables to Compare Ratios
6RP3a 4.5 Use Equivalent Ratios
6RP2 4.6 Find Unit Rates
6RP3b 4.7 Use Unit Rates
6RP3a 4.8 Equivalent Ratios & Graphs
6RP3c 5.1 Model Percents
6RP3c 5.2 Write Percent as Fraction & Decimal
6RP3c 5.3 Write Fractions and Decimal as Percent
6RP3c 5.4 Percent of a Quantity
6RP3c 5.5 Percents
6RP3d 5.6 Find the Whole froma Percent
6RP3d 6.1 Convert Units of Length
6RP3d 6.2 Convert Units of Capacity
Page 6 Unit Planning Guide: Grade 6 Unit 2 of 7 6RP3d 6.3 Convert Units of Weight & Mass
6RP3d 6.4 Transform Units
6RP3d 6.5 Distance, Rate & Time Formulas
NOTES:
19 Go Math lessons correspond to WPS Unit Guide 5
> MA RP3e (Solve problems that relate the mass of an object to its volume.) is not cited in WPS unit guide and is only partially covered by Go Math lesson 6.3
> lessons in bold print correspond to priority practice standards in WPS unit guide
> ***Order of WPS Unit guides was modified so that teaching of standards covered in WPS unit guide 5 immediately follow standards taught in WPS unit guide 2 (teaching of standards in unit guide 5 logically follows those taught in unit guide 2
Page 7 Unit Planning Guide: Grade 6 Unit 2 of 7 Math In Focus
Standard(s) Lesson Number Lesson Title Covered
6.RP.1, 6.RP.3d Chapter 4 Opener Ratio
6.RP.1, 6.RP.3d 4.1 Comparing Two Quantities
6.RP.3a 4.2 Equivalent Ratios
6.RP.3 4.3 Real-World Problems: Ratio
6.RP.1, 6.RP.3d Chapter 5 Opener Rates
6.RP.2, 6.RP.3 5.1 Rates and Unit Rates
6.RP.3, 6.RP.3b 5.2 Real-World Problems: Rates
6.RP.3, 6.RP.3c Chapter 6 Opener Percent
6.RP.3, 6.RP.3c 6.1 Understanding Percent
6.RP.3c 6.2 Fractions, Decimals, and Percents
6.RP.3c 6.3 Percent of A Quantity
6.RP.3c 6.4 *Real-World Problems: Percent
6.RP.3c 6.5 *Percent of Change *Lessons 6.4 and 6.5 also correlate with WPS Module 6
Page 8